This post analyzes who deserves the NFL’s Most Valuable Player award (spoiler alert: don’t read the title) based on some different criteria than most people have used. I want to focus on the word “valuable.”

There are many ways to interpret “valuable”, and you can reach very different conclusions based on how you define it. For me, valuable doesn’t mean best, most impressive, or most memorable. Value implies worth – the same production could be really valuable or worthless depending on how much it cost. An NFL team’s most precious commodity is its salary cap, so in any analysis of who has been the most valuable player, we have to account for how much salary cap they cost their team. We also must understand the replacement level of each position.

Think back to your last fantasy football draft. Kickers score more points than many players, but they have relatively little value partly because they all score about the same number of points. This idea holds true in the NFL: the best player at a replaceable position is not particularly valuable.

Applying these factors to the 2012 MVP race, we can better understand who really had the most valuable performances this season.

To quantify how much each player produced, I use Expected Points Added (EPA) from Advanced NFL Stats. Unfortunately, this method excludes individual offensive linemen, which is a limitation that doesn’t present a good solution. Sometime soon (I hope), we’ll have an accurate way to give offensive linemen their due credit. For now, however, I have to exclude the phenomenal seasons enjoyed by Joe Staley, Evan Mathis, John Sullivan, and many others.

To account for the replacement level, I first ranked each player by EPA within each position. I defined “replacement level” as the marginal starter at that position: the 33rd quarterback, running back, and tight end; the 65th wide receiver, defensive end, cornerback, and safety; the 49th defensive tackle and the 113th linebacker (assuming teams run a 4-3 and 3-4 defense each half of the time). Subtracting these values from every player’s EPA, we get their EPA Over Replacement (EPAOR).

All that’s left now is to divide each player’s EPAOR by his 2012 salary cap hit, provided by Spotrac. Here are the top 5 players in EPAOR per $100,000 of cap hit from this regular season:

Name

Position

Team

EPAOR per $100,000

Russell Wilson

QB

SEA

22.23

Danario Alexander

WR

SD

12.08

Eric Decker

WR

DEN

8.47

Randall Cobb

WR

GB

7.87

Stevie Brown

S

NYG

7.78

Russell Wilson dominates, and it’s not really close. He was twice as valuable as every other player in 2012 except for Danario Alexander, and Wilson was 84% more valuable than him.

What about the two guys that might actually win 2012 MVP? Peyton Manning and Adrian Peterson finished the regular season with 1.02 and 0.36 EPAOR/$100,000 (Ranked 172nd and 304th respectively). In terms of raw EPA, Manning did produce more than Wilson. However, that is the wrong way to approach the MVP award. We have to consider how replaceable production at a position is (in Peterson’s case, very replaceable) and cap hit ($544,850 for Wilson, $18,000,000 for Manning). Wilson contributed more to his team above the replacement level player per dollar than anyone else, making him the MVP of the 2012 season.

Hey Dan — I like this idea a lot, but I think it assumes that teams spend the “right” amount of money on each position, which is not necessarily true. I haven’t seen any research that shows how much a marginal EPAOR is to a team’s record (basically moving towards football’s WAR), which is what we really need to determine the dollar value of on-field production. I went for highest efficiency of EPAOR/dollar over raw total to avoid the issue, but agree that Value-Salary would be the best way to do it. – Kevin

The award doesn’t look at salary. You’ve defined valuable based upon dollar amount. The MVP trophy looks at value as only on the field production. The award you’ve given to Russell Wilson, deservingly so should be called “The player with the most dollar value.”

Cool idea. One thing you might want to incorporate the next time around is that the goal of an NFL team is not to spend 50% of the cap and go 9-7, but to spend 100% of the cap and be as good as possible. One of my favorite Brian posts was this one, noting that draft picks are more like gladiators than bricklayers (http://www.advancednflstats.com/2009/04/draft-picks-bricklayers-or-gladiators.html). This article seems to consider players as bricklayers. Even at $20M, by being the best QB in the league, Peyton Manning was pretty darn valuable.

Definitely true. If Manning is actually worth $40 million, that $22 million surplus value is incredible for Denver. As I mentioned in replying to Dan (above), until we find a way to accurately measure that “true value”, our analysis will be limited.

After I wrote the post though, I did sort of wonder whether calling a player “most valuable” based on his salary might be giving credit to the wrong person. After all, a player is always going to want to earn as much as possible, so Russell Wilson’s low salary isn’t really anything he can control. It’s actually the GM that is responsible for collecting good players at low cap numbers.

To get to Chase’s point, teams all have to work under the salary cap, and the cap now has mandatory minimums (I think that was part of the new CBA) so teams are all interested in maximizing their $/WP.

I think another point in Kevin’s favor as it relates to this post is that if you were going to put both Manning and Wilson on the trading block at their current cap numbers, I suspect that Wilson would draw more in a trade. I don’t know, that’s just a guess and I’m sure there would be people who would disagree with me.

I think another thing to consider is that if you tried to isolate value based on whose receivers were better, Wilson was throwing to a receiving corps that might be in the bottom half of the league, while Manning was throwing to probably a top 5 (or so) receiving corps.

Frank — didn’t see that article until you posted it here. Looks like we agree. I like your point that giving Russell the MVP is almost like saying “Congratulations, you are the most underpaid player in the NFL!” I liked looking at this fairly static debate from a different perspective though, and thought it was a useful way to rethink what we mean by “value”.

I think the comments above have a point. I’m guessing you are an Econ concentrator so you’ve studied Net Present Value and Internal Rate of Return. Your measure is basically a variant on IRR, it tells you how much value you get for each dollar you invest. The alternative metrics are like NPV, they tell you how much value you netted by subtracting out the opportunity cost.

There’s a great example people like to use to illustrate why generally NPV is preferred. Let’s set the discount rate to 3% for the rate we’ll say you’d get on long-term riskless bonds. Suppose you could choose between two investments, one that costs $1 million today and returns $1.5 million next year and one that costs $100,000 today and returns $500,000 next year.

IRR for project 1: 50%
IRR for project 2: 400%

Project 2 blows project 1 out of the water. It’s like Russell Wilson.

But consider how much money you would have in the end if you started with $1,000,000 and choose between option 1 and option 2, investing the leftovers on bonds.

Project 1: $1.5 million
Project 2: $1.427 million

So most people focus on NPV-like measures instead of IRR-like measures because the objective is to make money (win games), not to get a high rate of return on each $ invested (win lots of games per $ invested).

Also, the EPA per $1 million in cap number is <1 so the "bias" from leaving it out in discussion of value isn't that big. Even in the extreme case of Manning vs Wilson you're talking about giving Wilson a +18 handicap. Just ranking players by EPA pretty much gives you the list as using net EPA.

Steve — Thanks for your thoughts. I think to do something like NPV, you’d need to find how much a marginal EPA is worth in cap dollars. I know Brian has done some work on this problem (http://www.advancednflstats.com/2012/01/how-much-does-win-cost.html), but this measures the market value of a marginal EPA instead of the true impact of EPA on winning football games.

There’s been enough interest from everyone here I’ll take a crack at converting EPA to wins to cap hit. If anyone has seen analysis of this, please post it!

I looked at it using the “uncapped” year of 2010 since, in years where the cap is in place its not clear where the variation in cap numbers comes from and how to interpret it. Even for 2010 though I think the way bonuses are amortized into cap number hits is misleading so these data are noisy which will bias down the coeffs.

With the small sample size regressions of cap number on EPA, WPA, and GWP (from AdvancedNFLStats) are, unsurprisingly, insignificant but they’re all positive.

Each million in cap number is worth .77 EPA and 0.02 wins (using either WPA or GWP) over the season.

When you throw out Washington, which is a major outlier for some reason (Albert Haynesworth?), those numbers rise to 1.43 and 0.035.

The 95% CI on EPA goes up to 2.6 and 3.5 (w/o Washington) so its possible that extra $17.5 million Wilson saved for his team helped by 45 points (in expectation) but its probably more like 13 points.

One last thought here – given that football is a violent sport played by rosters of 53, I think there is an argument to be made for using your salary cap broadly across your value producing positions (yes QB, yes CB, yes DE, no to RB), rather than have it concentrated in a single player. For instance, while Manning’s money was not guaranteed this year (my recollection, not 100% sure) and it worked out fine, maybe if you play the 2012 season 100 or 1000 times, his neck or arm strength become an issue in a percent of those instances. Then in the alternate realities where an injury becomes an issue for the player you’ve invested so much in, your season is a total loss (see Colts 2011 season).

Basically what I’m getting at here is a risk concentration issue. Large salaries mean you have a lot of the value of your team tied up in a single player, which is, to steal a term from Taleb, a fragile way to construct your team.